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Lett."],"published-print":{"date-parts":[[2026,8,1]]},"abstract":"<jats:p>Dispersed fringe sensing (DFS) is an efficient co-phasing method for segmented mirrors, though conventionally limited to one-dimensional piston measurement. We propose a two-stage orthogonal decoupling method based on the multi-trace Hilbert transform. By combining frequency-domain carrier isolation with spatially robust fitting, this approach enables full-dimensional pose error retrieval using a standard DFS. Simulations show that under a signal-to-noise ratio (SNR) of 5\u2009dB, the piston retrieval error is below 0.6\u2009nm, and the tip-tilt error is within 0.5 \u03bcrad. Experimental validations yield an average piston retrieval error of 50.67\u2009nm, with absolute tip and tilt errors below 0.63 \u03bcrad and 0.70 \u03bcrad, respectively. 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